// revised Feb. 9, 1998

--------  C functions for calculating the NSA Ratings Curve -----

(Also available at <http://math.unm.edu/~rparker> )

//  C functions for calculating the NSA Ratings Curve
//          (The cumulative normal distribution)
// To find P(Win|Rating1,Rating2), as used in the NSA ratings
// formula (as of Jan. 10, 1998), call
//     NSARatingsCurve(Rating1-Rating2)

double NSARatingsCurve(double diff)
{
if (diff >  700)
   diff= 700;
if (diff < -700)
   diff=-700;
return(CumNormal(diff,0,200*sqrt(2)));
}

double CumNormal(double x, double mean, double stddev)
// The cumulative normal distribution
{
return(CumStandardNormal((x-mean)/stddev));
}

double CumStandardNormal(double x)
// The cumulative standard normal distribution
{
return( (1.0 - 0.5*erfcc(x/sqrt(2.0))) );
}

// erfcc() from the book __Numerical Recipes__
// Press, Flannery, Teukolsky, & Vetterling,
// Cambridge University Press, Cambridge, 1988
//
//
// erfcc() constants:
#define ERFCC_1  -1.26551223
#define ERFCC_2   1.00002368
#define ERFCC_3   0.37409196
#define ERFCC_4   0.09678418
#define ERFCC_5  -0.18628806
#define ERFCC_6   0.27886807
#define ERFCC_7  -1.13520398
#define ERFCC_8   1.48851587
#define ERFCC_9  -0.82215223
#define ERFCC_10  0.17087277
double erfcc(double x)
// from the book __Numerical Recipes__
// modified by Robert L. Parker
{
double t,z,ans;
z=fabs(x);
t=1.0/(1.0+0.5*z);
ans=t*exp(-z*z+ERFCC_1+t*
              (ERFCC_2+t*
              (ERFCC_3+t*
              (ERFCC_4+t*
              (ERFCC_5+t*
              (ERFCC_6+t*
              (ERFCC_7+t*
              (ERFCC_8+t*
              (ERFCC_9+t*
               ERFCC_10)))))))));
return  x >= 0.0 ? ans : 2.0-ans;
}